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The Philosophy of Vacuum Part 26. Physicists will find it extremely interesting, covering, as it does, technical subjects in an accessible way. For those with the necessary expertise, this book will provide an illuminating and authoritative exposition of a many-sided subject." -John D. Barrow, Times Literary Supplement. | Vacuum or Holomovement 243 -Z 20 n k Furthermore 0 j j 21 j a e j 22 so that if we identify with xy we have x Xj j Xjy 23 and 24 These results are exactly what one would expect from the usual approach to quantum mechanics. We are now in a position to discuss the relational notion of locality within the algebraic structure. The holomovement is a structure of activity with no a priori notion of absolute locality within it. In fact it should be regarded as a-local. In the example of the Weyl algebra we chose a particular local order by giving special significance to the element e . Thus we have essentially imposed a local order on the space. This order is arbitrary since it is possible to make an inner automorphism and produce a new set of generalized points with a new neighbourhood operator. Thus for example we can define a new set of generalized points e e- Z Z1 25 where Z is some element of . These space points will also have a corresponding dual momentum space e . In fact there are many such inner automorphisims in the algebra. Each will have its own unique order and therefore its own neighbourhood relation. If we use a neighbourhood element to define locality then there exist many different locality relations each related to another by an inner automorphism. We can also bring these ideas out within the present formalism of quantum mechanics by examining the Schrodinger representation in the same spirit. The principle of locality is built into this representation through the fact that the dynamical operators are functions of x and 8 dx. Furthermore it is the requirements of continuity and 244 B. J. Hiley single-valuedness of all physically significant operators that give rise to the correct energy levels and transition probabilities. Thus the Schrodinger representation has built into it a notion of locality whereas the Heisenberg representation and hence the algebraic approach does not. In order to make the latter completely equivalent to the Schrodinger .
